Turning Data into Information with the SVD


Satellites, sensors, cameras, scanners, computer simulations 
are creating or capturing huge amounts of data.  Data miners
seek the "gold" in these mountains of trash and trivia.

The data might come from:
* a system governed by well-known PDE's, or
* a collection of snapshots (literally!), or
* the tracks from the latest Gnarls Barkley album.  

In every case, we can try techniques of reduced order 
modeling, and hope to detect underlying patterns and
information.  The SVD (singular value decomposition)
is one of the simplest such techniques to apply, and
can help to express what the data is "trying to tell us".

In this talk, we will consider the analysis of data from
a fluid flow simulation, and show how the singular value
decomposition can expose underlying "designs" in the flow.
We will even see that these "designs" can be used as a
technique for further analysis of new fluid flow problems.

We will also discuss a facial recognition task, which begins 
with 600 photographs, and tries to answer the questions 
* "What do these faces have in common?", 
* "Is this a new picture of a face I've already seen?"
* "Is this a picture of a face or a pumpkin?"